package project.euler;

/**
 * A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
 * a^(2) + b^(2) = c^(2)
 * For example, 3^(2) + 4^(2) = 9 + 16 = 25 = 5^(2).
 * There exists exactly one Pythagorean triplet for which a + b + c = 1000.
 * Find the product abc.
 * 
 * <a href="http://projecteuler.net/index.php?section=problems&id=9">Problem 9</a>


 * @author Shekhar
 *
 */
public class PE9 {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		StopWatch stopWatch = new StopWatch();
		stopWatch.start();
		for(int c = 1000;c>0;c--){
			for(int b = c-1;b >0;b--){
				for(int a = b-1;a>0;a--){
					if( ( (a+b+c)== 1000) && (a*a + b*b -c*c == 0))  {
						System.out.println("a: "+a +", b: "+b +", c: "+c +" \na*b*c= "+a*b*c);
					}
				}
			}
		}
		System.out.println("Time Taken: "+ stopWatch.stop()+" ms");
	}

}
